What is the value of (cos²67° - sin²23°)?

We use the trigonometric identity cosθ = sin(90° - θ).
So, cos67° = sin(90° - 67°) = sin(23°) ⇒ cos²67° = sin²23° ⇒ cos²67° - sin²23° = 0
The value of the given expression is 0